Billboard "Reviews"...and a tad more
As mentioned elsewhere in this site, Billboard Magazine was (
and still is) the record industry "newspaper" for over
100 years! One of it's regular features is listing that weeks releases and reviews some of the more bigger releases.

'Xanadu', both singles and album, were one of the bigger releases for 1980 and the following is a complete list of
the magazine's reviews.
Billboard, May 24, 1980
Billboard, June 28, 1980
Billboard, August, 2, 1980
Billboard, August 9, 1980
Billboard October 18, 1980
not a review, but a banner the magazine provided during 'Magic's no. 1 single status.
ABOVE; this is an ad MCA Records put out on a monthly basis
announcing that months releases and for the week of July 5,
1980...Xanadu was included!

RIGHT: This article is included on the page in a form of a
correction. In the 'The Xanadu Story', I mentioned a lawsuit over a
dance step just before the movie's release. Well, I got that part
wrong; it was over a piece of music and here's the actual article.